Between-subjects statistics are used when comparing independent groups on an outcome. Independent groups means that the groups are "different" or "independent" from each other according to some characteristic. With between-subjects designs, participants can only be part of one group (independence) and only observed once (independence of observations, IOO).
One chooses a between-subjects statistical test based on the following:
1. Number of independent groups being compared (one group, two groups, or three or more groups)
2. Scale of measurement of the outcome (categorical, ordinal, or continuous)
3. Meeting statistical assumptions (independence of observations, normality, and homogeneity of variance)
Here is a list of between-subjects statistical tests and when they are utilized in applied quantitative research:
1. Chi-square Goodness-of-fit - One group, categorical outcome, a priori hypothesis for dispersal of outcome
2. One-sample median test - One group, ordinal outcome, a priori hypothesis for median value
3. One-sample t-test - One group, continuous outcome, meet the assumption of IOO and normality, a priori hypothesis for mean value
4. Chi-square - Two independent groups, categorical outcome, and chi-square assumption (more than five observations in each cell)
5. Fisher's Exact test - Two independent groups, categorical outcome, and when the chi-square assumption is not met
6. Mann-Whitney U - Two independent groups, ordinal outcome, and when the assumption of homogeneity of variance for independent samples t-test is violated
7. Independent samples t-test - Two independent groups, continuous outcome, meet the assumption of IOO, normality (skewness and kurtosis statistics), and homogeneity of variance (also known as homoscedasticity, tested with Levene's test)
8. Unadjusted odds ratio - Three or more independent groups, categorical outcome, chi-square assumption, choose a reference category and compare each independent group to the reference
9. Kruskal-Wallis - Three or more independent groups, ordinal outcome, and when the assumption of homogeneity of variance is violated
10. ANOVA - Three or more independent groups, continuous outcome, meet the assumption of IOO, normality, and homogeneity of variance
One chooses a between-subjects statistical test based on the following:
1. Number of independent groups being compared (one group, two groups, or three or more groups)
2. Scale of measurement of the outcome (categorical, ordinal, or continuous)
3. Meeting statistical assumptions (independence of observations, normality, and homogeneity of variance)
Here is a list of between-subjects statistical tests and when they are utilized in applied quantitative research:
1. Chi-square Goodness-of-fit - One group, categorical outcome, a priori hypothesis for dispersal of outcome
2. One-sample median test - One group, ordinal outcome, a priori hypothesis for median value
3. One-sample t-test - One group, continuous outcome, meet the assumption of IOO and normality, a priori hypothesis for mean value
4. Chi-square - Two independent groups, categorical outcome, and chi-square assumption (more than five observations in each cell)
5. Fisher's Exact test - Two independent groups, categorical outcome, and when the chi-square assumption is not met
6. Mann-Whitney U - Two independent groups, ordinal outcome, and when the assumption of homogeneity of variance for independent samples t-test is violated
7. Independent samples t-test - Two independent groups, continuous outcome, meet the assumption of IOO, normality (skewness and kurtosis statistics), and homogeneity of variance (also known as homoscedasticity, tested with Levene's test)
8. Unadjusted odds ratio - Three or more independent groups, categorical outcome, chi-square assumption, choose a reference category and compare each independent group to the reference
9. Kruskal-Wallis - Three or more independent groups, ordinal outcome, and when the assumption of homogeneity of variance is violated
10. ANOVA - Three or more independent groups, continuous outcome, meet the assumption of IOO, normality, and homogeneity of variance
